Related papers: Mathematical Models in Schema Theory

We develop a purely set-theoretic formalism for binary trees and binary graphs. We define a category of binary automata, and display it as a fibred category over the category of binary graphs. We also relate the notion of binary graphs to…

Foundation models have emerged as critical components in a variety of artificial intelligence applications, and showcase significant success in natural language processing and several other domains. Meanwhile, the field of graph machine…

Schematic maps are in daily use to show the connectivity of subway systems and to facilitate travellers to plan their journeys effectively. This study surveys up-to-date algorithmic approaches in order to give an overview of the state of…

Geospatial sciences include a wide range of applications, from environmental monitoring transportation to infrastructure planning, as well as location-based analysis and services. Graph theory algorithms in mathematics have emerged as…

Complex networks or graphs are ubiquitous in sciences and engineering: biological networks, brain networks, transportation networks, social networks, and the World Wide Web, to name a few. Spectral graph theory provides a set of useful…

With traditional computing technologies reaching their limit, a new field has emerged seeking to follow the example of the human brain into a new era: neuromorphic computing. This paper provides an introduction to neuromorphic computing,…

In this paper we will present the two basic operations for database schemas used in database mapping systems (separation and Data Federation), and we will explain why the functorial semantics for database mappings needed a new base category…

Artificial intelligence has made great strides in the last decade but still falls short of the human brain, the best-known example of intelligence. Not much is known of the neural processes that allow the brain to make the leap to achieve…

Graphs, and sequences of growing graphs, can be used to specify the architecture of mathematical models in many fields including machine learning and computational science. Here we define structured graph "lineages" (ordered by level…

Presenting systems of differential equations in the form of diagrams has become common in certain parts of physics, especially electromagnetism and computational physics. In this work, we aim to put such use of diagrams on a firm…

In this paper we develop a structure called Link Algebra, in which we present a Set with two binary operations and an axiom system developed from the study of graph theory and set/antiset theory, sowing main theorems and definitions. Once…

This paper introduces a biomathematical model designed to describe the internal dynamics of dream formation and spontaneous cognitive processes. The model incorporates neurocognitive factors such as dissatisfaction, acceptance, forgetting,…

In psychiatry, we often speak of constructing "models." Here we try to make sense of what such a claim might mean, starting with the most fundamental question: "What is (and isn't) a model?". We then discuss, in a concrete measurable sense,…

Graph reachability is the task of understanding whether two distinct points in a graph are interconnected by arcs to which in general a semantic is attached. Reachability has plenty of applications, ranging from motion planning to routing.…

There have been rapid developments in model-based clustering of graphs, also known as block modelling, over the last ten years or so. We review different approaches and extensions proposed for different aspects in this area, such as the…

The integration of knowledge extracted from different models described by domain experts or from models generated by machine learning algorithms is strongly conditioned by the lack of an appropriated framework to specify and integrate…

In fact, there exist three genres of intelligence architectures: logics (e.g. \textit{Random Forest, A$^*$ Searching}), neurons (e.g. \textit{CNN, LSTM}) and probabilities (e.g. \textit{Naive Bayes, HMM}), all of which are incompatible to…

A complete understanding of the brain requires an integrated description of the numerous scales of neural organization. It means studying the interplay of genes, synapses, and even whole brain regions which ultimately leads to different…

We present a mathematical and philosophical framework in which brain function is modeled using sheaf theory over neural state spaces. Local neural or cognitive functions are represented as sections of a sheaf, while global coherence…

These lecture notes cover basic automata-theoretic concepts and logical formalisms for the modeling and verification of concurrent and distributed systems. Many of these concepts naturally extend the classical automata and logics over…